Position Of Maximum Stress Research Articles

Diffusion-induced stresses in a long bar under an electric field

Diffusion-induced stresses in a long bar with a square cross section under an electric field are calculated. We obtain in advance analytical solutions of the concentration, then with these results, the diffusion-induced stresses are also calculated analytically by introducing the displacement potential and Airy stress function. The results show that the electric field can depress the stresses and deviate the positions of local maximum stresses, and these effects are more apparent at short times than at long times.

一様曲げ変形（モーメント軸が流れ方向）を受ける段ボールの応力解析 第４報 厚さ方向に非対称な強度をもつ両面段ボールの場合

Analysis of the bending stress in single wall corrugated fiberboard (SWCF) with asymmetrical strength distribution for the thickness direction (normal to the kraft-liner (KL)) is performed, and relations between maximum of absolute stress σ smax, σk1max and σk2max and shape for upper KL (KL1), lower KL (KL2) and SMP medium (CM, (thickness Ts : wavelength L : wave height h)) are discussed. Then relations between strength Efs, Efk1 and Efk2 per mass and shape factor are obtained.(1) Distance h0 between neutral surface and thickness for SWCF moves to KL1 side with the increase of Young's modulus Ek1 and thickness Tk1 of KL1. h0 decreases obviously with the increase of Ts and increases with the increase of h. And h0 increases gradually with the increase of L.(2) Positions of maximum stress for CM and KL move to KL2 side with increase of Young's modulus Ek1 and thickness Tk1 of KL1. Their maximum stresses for CM and KL are on the other outer surfaces.(3) σ smax, σk1max and σk2max decrease with the increase of the thickness Ts and wave height h for CM. σsmax, σk1max and σk2max increase initially and then decrease with the increase of the wavelength L for CM. Then the maximum values appear with the increase of L.(4) Efs decreases with the increase of Ts, and increase with the increase of L and h. Efk1 and Efk2 increase with increase of Ts and h, and decrease with the increase of L.

The Fractures of Graphite Cylinders with a Transverse Hole under Torsion.

This study aimed at a theoretical approach which can be applied to the Fracture analysis of graphite cylinders with a transverse hole under torsion. It was found that the position of maximum tensile stress occurred at an intersection of hole and outer surface of the cylinder. Theoretical analysis has been carried out with the surface layer theory applied to the maximum tensile stress at the edge of the hole. The graphite is brittle material with a little ductility; therefore, we established the fracture criteria by taking the ductility into account. The fracture stresses of the solid and hollow cylinders were dependent only on the diameter of the hole, and were not influenced by the outer diameter of the cylinder. A hole with the comparatively small diameter had no effect on the fracture stress of the cylinder.

Analysis of Offshore Structural Dynamics with Nonproportional Damping

A method of analysis of the nonproportionally damped motions of fixed offshore structures in waves is presented. The damping considered is that due only to radiation, and is assumed to be linear. Since both the radiation damping and the added mass are frequency dependent, the damping is, by nature, nonproportional. Hence, the standard normal‐mode analysis cannot be used. To isolate the modes, the matrix equation of motion of the assumed lumped‐mass system is first transformed into a first‐order equation. The complex eigenvectors and eigenvalues for the underdamped system are then obtained through matrix iteration, The displacement of each mass is obtained in deterministic seas. One of the most important results of this analysis is the demonstration of the ability of the technique to predict the movement of the nodal points over time. That is, the nodal points move up and down the centerline of the structure over each period. This means that the analyst can predict the positions of maximum stresses and str...

Dynamic stress analysis of plates of different kinds material.

Structures of machine parts subjected impact load often suffer unexpected damage, which is remarkably different from the observed in static cases. Generally, the reflection and interferference of stress-wave play an important role in dynamic cases, and it is desirable to study the time variation of the stress distribution, and especially the value of dynamic stress concentration factors around the boundaries of different kinds of materials. Hence, we analyzed stress propagation and dynamic stress concentration phenomena around the boundary of different kinds of materials in a plate by utilizing the strain gage method, the dynamic photoelastic method and also the finite element method. We found that two-dimensional dynamic stress concentration factors obtained by the present three methods are in general agreement and if the ratio of E2 (young's modulus for the different materials)/E1 (young's modulus for the matrix) is small, the dynamic stress concentration factor is small, but the position of maximum stress occurs at the circular bounday of the matrix. On the other hand, if the ratio of E2/E1 is large, the dynamic stress concentration factor is large, and the position of maximum stress occurs at the boundary of the circular hole in various types of materials.

Observation of slip dislocations in (100) silicon wafers after BF2 ion implantation and rapid thermal annealing

The generation of slip dislocations in BF2 ion-implanted, 100-mm-diam silicon wafers during rapid thermal annealing is investigated. Whole wafer x-ray topography shows that annealing at 1150 °C causes slip to initiate randomly at positions of maximum resolved stress at the wafer edges and over scribe marks made on the back surface prior to annealing. Lowering the annealing temperature by 20 °C, which corresponds to decreasing the silicon yield stress by less than 106 dyn cm−2, prevents slip from occurring and allows sufficient removal of implantation-induced defects from which junction diodes with good current-voltage characteristics are fabricated.

The helix angle factor of helical gears.

This paper presents a study on the helix angle factor in considering the difference between root stresses of the helical gear and its virtual spur gear in the normal section. The calculation of bending strength of the helical gear is commonly based on the virtual spur gear. The root stresses of helical gears with various helix angles, numbers of teeth and overlap ratios were calculated, and the meshing position of maximum root stress (worst loading position) was examined. On the basis of these results, the helix angle factor of helical gears was clarified, in which the effect of load distribution on the line of contact is taken into account. Furthermore, the helix angle factors used in the various formulas for the bending strength of helical gear were compared with the results obtained in this paper.

Effect of radial shaft clearance on root stress of planet gear.

This paper presents a study on the effect of radial clearance between a planet gear and shaft on the root stress of a planet gear. The stress analysis of planet gears with various radial shaft clearances by the 2-dimensional finite element method (FEM), in which the elastic contact between a planet gear and shaft was taken into consideration, was carried out under different normal tooth loads, and the relation between the root stress and normal tooth load, the effect of radial shaft clearance on root stress, the position of maximum root stress and the cyclic stress under running conditions were examined. Furthermore stress analysis of planet gears with various radial shaft clearances and rim thicknesses was carried out and the stress state of a planet gear with radial shaft clearance was clarified to a considerable extent.

Study on Bending Fatigue Strength of Helical Gears : 3rd Report, Mechanism of Bending Fatigue Breakage

In this paper, the relations between the stress distributions on root fillet and the crack initiation and propagation in helical gear, thin rim gear teeth and cantilever plate were examined and the mechanism of bending fatigue breakage of helical gears was investigated. It was found that a crack of helical gear teeth occurs at the position of maximum root stress on the tensile fillet and the directions of crack propagation differ in each normal section. Furthermore the existing testing methods of bending strength for helical gear teeth were compared on the basis of the experimental results.

A new look at the bending strength of gear teeth

This paper reports on an extensive two-dimensional photoelastic study of the basic deformation behavior of gear teeth under load. Limitations of existing bending-strength design procedures are used to formulate a test program which considers the magnitude of the critical root-fillet stresses, the effects of varying the load position on the flank, the effects of friction forces at contact and the relationship between bending and shearing deformations. Particular interest is devoted to a study of the observed movement of the maximum-stress position around the fillet as load moves up the tooth flank and to the associated variation in stress-concentration factors (around the fillets) due to radial, bending and shear loads. Note is also made of the problems associated with observed ‘proximity effects’ and of the procedures carried out in an attempt to qualify the nature of the effect.

An analysis of thermal stress fracture in a graphite electrode used in an arc steel making furnace

In this paper, the thermal stress in the graphite electrode, which is connected typically three rods of 20 in. dia., is analyzed by an elastic theory as an axially symmetrical thermal stress of cylinder with finite length. The axial and radial temperature distributions in electrode during the regular power (RP), high power (HP) and ultrahigh power (UHP) operations in arc steel making, are assumed with reference to the actual data of steel making arc furnace measured by Nedopil and Storzer. For the reason of convergency of analytical solution in the center of cylinder, the hollow cylinders with a small hole in the center are treated. These hollow cylinders are used partly at present because of the arc stability. The distributions of principal stress components were calculated numerically using the anisotropic mechanical properties of graphite at the temperature as a function of operating conditions of RP, HP and UHP. The results of hollow electrode with small hole obtained here may be extended to the case of solid electrode for the evaluations of maximum thermal stress which occurs at the outer surface of electrode. The values and the positions of maximum stresses are discussed in comparison with the anisotropic properties of mechanical strength of graphite, and are investigated the current carrying capacities of graphite electrode. These analytical results agree very well with the actual fracture phenomena of graphite electrode observed in a model arc furnace.

BUCKLING AND INITIAL POSTBUCKLING OF OVAL CYLINDRICAL SHELLS UNDER COMBINED AXIAL COMPRESSION AND BENDING*

AbstractBuckling and initial postbuckling of an oval cylindrical shell under pure bending and under combined uniform axial compression and bending is investigated. The first‐ and second‐order stability equations are developed from the Donnell‐type equations that are shown to be appropriate. The solution of these two sets of equations determines, respectively, the buckling characteristics and a “sensitivity parameter.” The buckling loads are found to be in good agreement with the engineering approximation based on the assumption that buckling occurs when the local axial stress equals that corresponding to the classical buckling stress of a locally equivalent circular cylindrical shell under uniform axial compression. Results also show that an oval cylinder can be stronger or weaker than the equivalent circular cylinder, depending on the orientation of the couples. However, in any case the oval shell is always found to be sensitive to imperfections; the greater the load‐carrying capacity, the greater the sensitivity.Furthermore, in contrast to the behavior of the circular and weak oval cylinders, buckling of the strong oval cylinder need not initiate at the position of maximum compressive stress.

Failure analysis of rolling bearings by X-ray measurement of residual stress

Residual stress measurements were carried out for the failure analyses of rolling bearings. According to the survey of more than one hundred examples, some change in residual stress was observed in most cases. Compressive residual stresses peak below the surface and if present, represent the position of maximum shearing stress due to normal contact pressure. Unexpected overloading is confirmed by this method. However, bearings often fail without such overloading. Early failures were observed to be associated with the residual stress changes near the surface. The influences of sliding, vibration and surface roughness on residual stress changes are discussed.

Analysis on Thermal Stress Fracture of Graphite Electrode for Steel Making Arc Furnace

In this paper, the thermal stress in the graphite electrode, which is connected typically three rods of 20" in diameter, is analyzed by an elastic theory as an axially symmetrical thermal stress of cylinder with finite length. The axial and radial temperature distributions in electrode during the regular power (RP), high power (HP) and ultrahigh power (UHP) operations in arc steel making, are assumed with reference to the actual data of steel making arc furnace measured by Nedopil and Storzer. For the reason of convergency of analytical solution in the center of cylinder, the hollow cylinders with a small hole in the center are treated. These hollow cylinders are used partly at present because of the arc stability. The distributions of principal stress components were calculated numerically using the anisotropic mechanical properties of graphite at the temperature as a function of operating conditions of RP, HP and UHP.The results of hollow electrode with small hole obtained here may be extended to the case of solid electrode for the evaluations of maximum thermal stress which occurs at the outer surface of electrode. The values and the positions of maximum stresses are discussed in comparison with the anisotropic properties of mechanical strength of graphite, and are investigated the current carrying capacities of graphite electrode. These analytical results agree very well with the actual fracture phenomena of graphite electrode observed in a model arc furnace.

Fatigue testing of short-link chain under line-loading conditions

Theory predicts that the position of maximum stress in short-link chain loaded elastically in tension is the crown, and this suggests that fatigue failures should occur there. In contrast, recent experimental work has shown that fatigue failures in these links occur at the junctions of intrados with straight sides, and photoelastic studies have confirmed that this is the position of maximum stress. This discrepancy is thought to be due to the fact that the theory assumes point loading between adjacent links and takes no account of ‘bedding down’ of the links. In the present work, bedding down has been minimized by the use of line loading, and crown failures have been obtained during fatigue cycling below the elastic limit.

Paper 2: Effect of Bending Moments on Nozzles with Forged Transition Pieces

An experimental study has been made of the elastic stress distributions arising in the vicinity of two transition rings of the type used to connect cylindrical ducts with large spherical pressure vessels. The effect of bending moments on the duct was considered and theoretical estimates of the stresses were made by modifying certain well-known analyses. Two of these methods gave results close to the experimental values in a region which included the position of maximum stress. This occurred near the weld between the spherical shell and the transition ring. In a further investigation it was found that, for the order of loads applied, the principle of superposition may be used to calculate the combined effect of a local bending moment and an internal pressure. When allowable bending moments at design pressure are calculated using a limiting stress concentration factor, the heavier transition piece is slightly superior to the other.

Burnout conditions for flow of boiling water in vertical rod clusters

AbstractThis paper deals with a new concept for predicting burnout conditions for forced convection of boiling water in fuel elements of nuclear boiling reactors.The concept states the importance of considering the ratio of heated channel perimeter to total channel perimeter.The perimeter ratio concept was arrived at from an experimental study of burnout conditions in rod clusters consisting of three rods of 13 mm. outside diameter and 830 mm. heated length. Data were obtained for pressures between 2.5 and 10 kg./sq. cm., surface heat fluxes between 50 and 120 W./ sq. cm., mass flow rates between 0.03 and 0.33 kg./sec., and steam qualities between 0.01 and 0.52.The rod clearance for the experiment were 2 and 6 mm. The diameter of the channel was 41.3 mm. Additional runs were also performed after unheated displacement rods were introduced in the channel. The rod clearance in this case was 6 mm.In the ranges investigated the measured burnout steam qualities at the outlet of the channel decrease with increasing heat flux and decreasing pressure. Furthermore it has been found that the influence of rod clearance is, in the range investigated, of small significance for engineering purposes.It has also been observed that the present burnout steam quality data for the rod clusters are much lower than those earlier obtained for round ducts. This may be explained physically by means of the perimeter ratio concept.It has also been found that the surface shear stress distribution around the channel perimeter and especially the position of maximum shear stress is of great importance for predicting burnout conditions for flow in channels.Finally the new method has helped in understanding and interpreting experimental results which earlier may have seemed inconsistent.

The Strength of Rails with Particular Reference to Rail Joints

This three-part paper describes recent work on rails carried out by the Research Department of British Railways. Part I details the rail sections considered, theoretical considerations of longitudinal bending strength and an analysis of failures in service. Part II describes a site investigation which was made into the dynamic stresses experienced by rail joints under traffic. Stresses in both flat bottom (F.B.) and bull head (B.H.) rail joints have been measured with both normal and abnormal conditions of sleeper packing. Electrical resistance strain gauges were used at the calculated positions of maximum stress in each fishbolt hole, and at other positions in the joint. The work initially covered the effects of steam locomotives and steam hauled stock, but was later extended to a second site so that electric locomotives and multiple unit electric stock could be similarly covered. The investigation brought out the marked influence of speed, wheel diameter and axle load on the magnitude of the stresses induced; and in view of the prospective increase in speeds, and the employment of diesel electric and electric locomotives with heavy axle loads on smaller wheels than as is usual currently, importance attaches to these results and their implications on the life expectancy of rail steel under fatigue loading. Part III describes fatigue tests which have been made on B.H. and F.B. rails, both plain and when drilled with fishbolt holes. The susceptibility to cracks starting at bolt holes, due to shear stresses in the web, is compared for the two rail sections, and some consideration is given to various methods of increasing the resistance to cracking of this type. It is shown that ordinary atmospheric corrosion greatly reduces the fatigue strength of rails, and any proposed method of reducing bolt hole failures must therefore take this into account.

Study on the Photoelastic Stress Determination of Plate Beams having Circular Arc Projections

The specimens of plate beams having a circular arc projection on one side or on either side symmetrically were prepared by an epoxy plate and the stress distribution under an uniform bending moment or the tensile load was studied by photo-elastic experiment. The results are as follows : The maximum stress always occurs near the root of the projection and the stress concentration factor at the maximum stress position in the plate beam having an arc projection on one side is larger than that having an arc projection on either side symmetrically, and then the factor under the tensile load is larger than that under the uniform bending moment. The factor α is affected by the height ΔH and the length θ of the arc projection, the radiue of curvature r at the root of the projection and the original breadth H of the plate beam. The smaller r/H, θ or the larger ΔH/H is, the larger α is obtained, and α increases suddenly when r/H is smaller than about 0.1.